Purpose: A series of all-atom molecular-level computational analyses is carried out in order to investigate mechanical transverse (and longitudinal) elastic stiffness and strength of p-phenylene terephthalamide (PPTA) fibrils/fibers and the effect various microstructural/topological defects have on this behavior. The paper aims to discuss these issues. Design/methodology/approach: To construct various defects within the molecular-level model, the relevant open-literature experimental and computational results were utilized, while the concentration of defects was set to the values generally encountered under prototypical polymer synthesis and fiber fabrication conditions. Findings: The results obtained revealed: a stochastic character of the PPTA fibril/fiber strength properties; a high level of sensitivity of the PPTA fibril/fiber mechanical properties to the presence, number density, clustering and potency of defects; and a reasonably good agreement between the predicted and the measured mechanical properties. Originality/value: When quantifying the effect of crystallographic/morphological defects on the mechanical transverse behavior of PPTA fibrils, the stochastic nature of the size/potency of these defects was taken into account.